[HN Gopher] What does the "mean" really mean?
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What does the "mean" really mean?
Author : max_
Score : 28 points
Date : 2021-07-26 08:39 UTC (1 days ago)
(HTM) web link (arxiv.org)
(TXT) w3m dump (arxiv.org)
| humanistbot wrote:
| What I got out of this was: Everyone knows that the mean and
| median are different ways of summarizing a distribution, which
| have different purposes. But did you know there are many
| different kinds of means too? The one you think of when you use
| "mean" is the arithmetic mean. But there are weighted means,
| geometric means, and harmonic means. The straightforward
| arithmetic mean isn't always the best way of summarizing the
| center of a distribution, even though it is conceptually the
| simplest and the way we've always done it.
| bethecloud wrote:
| The mean is just another magic number
| shoto_io wrote:
| Is this really meaningful?
| minikites wrote:
| I think it's helpful to general number literacy to know about
| the different types of mean and in which situations they are
| applicable:
|
| https://en.wikipedia.org/wiki/Geometric_mean#Applications
|
| https://en.wikipedia.org/wiki/Harmonic_mean#Examples
| jwilber wrote:
| Seems far to philosophical to be useful in my opinion.
| nanis wrote:
| > average is merely an abstraction which has meaning only within
| its mathematical set-up.
|
| And probability is just a normalized denumerably additive measure
| over a sigma algebra.
|
| We've done very well constructing theories on the basis of these
| definitions, but it is useful to remember that neither has
| empirical content.
| derbOac wrote:
| Nice little paper, although maybe a little stilted. It's a good
| idea to think about these basic quantities a bit more deeply and
| why you might want to use one measure of central tendency more
| than another. It's good to have a solid rationale for it, and I
| thought this was a nice brief overview of some perspectives I
| wasn't aware of.
|
| For some reason I thought the mean could be thought of as a
| single number that is most representative of a sample or
| population in an information loss (algorithmic/kolgomorov
| complexity, maybe relative entropy?) sense, or maximum likelihood
| sense (maybe under some distributional constraints?). I might be
| misremembering that though, and it's difficult to figure out the
| right search terms to track it down.
| michael1999 wrote:
| In many systems, the mean really does summarize the whole. E.g.
| kinematics works just fine using the mean point mass for solids
| (i.e. the centre-of-gravity) in place of the whole.
| kergonath wrote:
| It's an approximation, though. You can't really describe a
| rotating body looking only at its centre of mass. So it does
| summarise the whole in the sense that we choose to ignore what
| it cannot describe and live with it, but it's more a matter of
| convenience than a profound meaning.
| morei wrote:
| No, that's exactly the point. Knowing the center of mass and
| the moment of inertia is sufficient: You don't know need to
| know the exact shape, or the variations in density inside the
| object etc etc.
| kergonath wrote:
| Yes, the centre of mass and the moment of inertia, i.e.,
| not only the centre of mass. The moment of inertia depends
| on the shape of the object.
| ndr wrote:
| And so does the centre of mass' position...
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